Question 42: Atoms & Nuclei

Question

The radius of a nucleus as measured by electron scattering is $$4.8 \mathrm{~fm}$$. The mass number of nucleus is most likely to be

Accepted Answer

To determine the mass number, we use the empirical formula for the nuclear radius:
$$R = R_0 A^{\frac{1}{3}}$$
where:
Ã¢ÂÂ¢ $$R$$ is the measured nuclear radius,
Ã¢ÂÂ¢ $$R_0 \approx 1.2 \, 	ext{fm}$$ is a constant, and
Ã¢ÂÂ¢ $$A$$ is the mass number.
Step-by-step, we have:
Substitute the given radius:
$$4.8 \, 	ext{fm} = 1.2 \, 	ext{fm} \cdot A^{\frac{1}{3}}$$
Solve for $$A^{\frac{1}{3}}$$:
$$A^{\frac{1}{3}} = \frac{4.8}{1.2} = 4$$
Cube both sides to find $$A$$:
$$A = 4^3 = 64$$
Thus, the mass number is most likely 64, which corresponds to Option C.

Answer

46

Answer

16

Answer

64

Answer

48

Atoms & Nuclei

The radius of a nucleus as measured by electron scattering is $4.8 \mathrm{~fm}$. The mass number of nucleus is most likely to be

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